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\int\frac{37-11x}{\left(x^2-x-2\right)\left(x-3\right)}dx

Integral of (37-11x)/((-1x-2+x^2)(x-3))

Answer

$\ln\left|x-3\right|+4\ln\left|1+x\right|-5\ln\left|x-2\right|+C_0$

Step-by-step explanation

Problem

$\int\frac{37-11x}{\left(x^2-x-2\right)\left(x-3\right)}dx$
1

Factor the trinomial $\left(-2-x+x^2\right)$ finding two numbers that multiply to form $-2$ and added form $-1$

$\begin{matrix}\left(-2\right)\left(1\right)=-2\\ \left(-2\right)+\left(1\right)=-1\end{matrix}$

Unlock this step-by-step solution!

Answer

$\ln\left|x-3\right|+4\ln\left|1+x\right|-5\ln\left|x-2\right|+C_0$
$\int\frac{37-11x}{\left(x^2-x-2\right)\left(x-3\right)}dx$

Main topic:

Integrals by partial fraction expansion

Used formulas:

5. See formulas

Time to solve it:

~ 0.91 seconds